How does SGP know what direction and how much to move the telescope to “center”? I do not see where there is a calibration of this. If it finds that moving in a certain direction increases the error, does it reverse direction? Or, does it just fail?
Centering uses plate solving. That essentially removes the need for any calibration as we’re not nudging, we’re slewing.
I am not sure I understand. You seem to be saying that SGP uses the GoTo capabilities of the scope to precisely position itself. That would only seem to work if SGP plate solves an image after a GoTo and then sync’s the telescope to that solved position and issues another GoTo to the desired coordinates and repeats this loop until hopefully the nearness criterion is met.
Is that what is happening? If it is not "sync"ing, then, I don’t understand how it works if it is not nudging.
That’s exactly how it works. Try it and see what happens.